Wednesday

April 16, 2014

April 16, 2014

**Recent Homework Questions About Calculus**

Post a New Question | Current Questions

**Calculus**

Find the area cut off by x=4 from the hyperbola x^2/9-y^2/4=1. Answer is 4.982 in the book. I have proceeded as under: Y=2/3*sqrt(x^2-9) and rhe reqd. area is double of integral 2/3*sqrt(x^2-9) from 3 to 4. Int= 2/3*[xsqrt(x^2-9)/2 – 9/2*log{x+sqrt(x^2-9)}] from 3 to 4 =x...
*Friday, March 28, 2014 at 2:17am*

**Calculus Help Please!!!**

One of us made an arithmetic mistake. It is up to Tanya to get it right :)
*Thursday, March 27, 2014 at 9:06pm*

**Calculus Help Please!!!**

According to Newton's Law of Cooling T(t) = roomtemp + (37 - 20)e^(-kt) , where t is the time in hours and k is a constant so we get two equations: 32.5 = 20 + 17e^(-kt) ---> 12.5 = 17e^(-kt) and 30.3 = 20 + 17e^(-k(t+1)) ---> 10.3 = 17e^(-kt - k) divide them: 115/...
*Thursday, March 27, 2014 at 9:02pm*

**Calculus Help Please!!!**

rate of change of temp proportional to temp above room temp which is 20 to make it easy on the arithmetic define T' = real T - 20 dT'/dt = k (T') dT/T' = k dt ln T' = k t T' = C e^kt let's call t = 0 at 1:30 T = 32.5 so T' = 12.5 12.5 = C e^0 = ...
*Thursday, March 27, 2014 at 8:54pm*

**Calculus Help Please!!!**

I am going to assume it is algebra first take t = 0 at 1:30 T = Ti - k t Ti = 32.5 so T = 32.5 - k t 30.3 = 32.5 - k (1 hour) k = 2.2 so T = 32.5 - 2.2 t 37 = 32.5 - 2.2 t t = - 2.04 call it 2 hours so by that linear model 11:30 am now I will work on the more realistic ...
*Thursday, March 27, 2014 at 8:38pm*

**Calculus Help Please!!!**

Are you sure this is calculus? You want exponential decay to room temp? Or is it algebra and you want a linear function?
*Thursday, March 27, 2014 at 8:30pm*

**Calculus Help Please!!!**

In a murder investigation, the temperature of the corpse was 32.5 C at 1:30pm and 30.3 C an hour later. Normal body temperature is 37.0 C and the temperature of the surrounding was 20.0 C. When did the murder take place? PLEASE SHOW STEP BY STEP
*Thursday, March 27, 2014 at 8:16pm*

**Calculus**

best use radians, pi/2
*Thursday, March 27, 2014 at 3:20pm*

**Calculus**

when t=90?
*Thursday, March 27, 2014 at 2:59pm*

**Calculus**

y" = 5cos(t) so, when is that zero?
*Thursday, March 27, 2014 at 2:52pm*

**Calculus**

A weight oscillates in a vertical motion according to the position function y(t)=-5 cos(t). Assuming t≥0, when will the acceleration if the weight be zero for the first time?
*Thursday, March 27, 2014 at 2:51pm*

**Calculus**

-9.8 m/s^2
*Thursday, March 27, 2014 at 2:45pm*

**Calculus**

An object in free fall has its distance from the ground measured by the function d(t)=-4.9t^2 +50, where d is in meters and t is in seconds. If gravity is the only acceleration affecting the object, what is gravity's constant value?
*Thursday, March 27, 2014 at 2:37pm*

**Calculus**

Ahh. I see that I was interpreting 243^3/5 as (243^3)/5
*Thursday, March 27, 2014 at 12:05pm*

**Calculus**

just using ln a^b = b ln a ln (243^3/5 *32^4/5) = ln ( (3^5)^(3/5) * (2^5)^(4/5) ) = ln ( 3^3 * 2^4) = ln (27*16) = ln(432) 1/5 ln (243^3 * 32^4) = ln [ (243^3 * 32^4) ^(1/5) ] = ln (243^(3/5) * 32^(4/5) ) = .... = ln(432)
*Thursday, March 27, 2014 at 12:01pm*

**Calculus**

No one is bothered by the fact that 5 does not divide powers of 2 and 3?
*Thursday, March 27, 2014 at 11:37am*

**Calculus**

same as y": -cosx
*Thursday, March 27, 2014 at 11:25am*

**Calculus**

If y=cos x, what is y^(6) (x)?
*Thursday, March 27, 2014 at 11:18am*

**Calculus**

I agree with Damon's "huh" since ln (243^3/5 *32^4/5) = 1/5 ln (243^3 * 32^4)
*Thursday, March 27, 2014 at 10:30am*

**CALCULUS problem**

int x^-3 dx = -.5 x^-2 + c at x = 3 = -.5/9 at x = 1 = -.5 so A = .5 - .5/9 = .5(8/9) = 4/9 B at x = h int = -.5/h^2 right half = -.5/9 +.5/h^2 left half = -.5 h^2 +.5 so -.5 h^2 + .5 = -5/9 +.5/h^2 1/h^2 = .5 + 5/9 = 4.5/9 + 5/9 = 9.5/9 = 19/18 int 1 to 3 of pi (x^-6)dx = -pi...
*Thursday, March 27, 2014 at 9:53am*

**CALCULUS problem**

There are four parts to this one question, and would really appreciate if you could show and explain how you get to the answer, because I tried looking up how to find the answer myself, but nothing made sense. Thank you! 11. The region R is bounded by the x-axis, x = 1, x = 3...
*Thursday, March 27, 2014 at 8:51am*

**Calculus**

huh?
*Thursday, March 27, 2014 at 7:51am*

**Calculus**

good except for this step: ln (243^3/5 *32^4/5) should be 1/5 ln (243^3 * 32^4)
*Thursday, March 27, 2014 at 5:36am*

**Calculus**

The hands of a clock in some tower are 4.5m and 2m in length. How fast is the distance between the tips of the hands changing at 9:00 at time t hours after 12:00, (at t=0) the minute hand is at 4.5 sin(2pi*t) the hour hand is at 2.0sin(2pi*t/12) at 9:00, the distance d is d^2...
*Thursday, March 27, 2014 at 5:34am*

**Calculus**

x = ln 243 y = ln 32 LET Z = e^((3x + 4y)/5) ln [z ]= (3x+4y)/5 ln z = (1/5)( 3 ln 243 + 4 ln 32) = ln (243^3/5 *32^4/5) = ln (27*16) = ln(432) if ln z = ln 432 then z = 432
*Thursday, March 27, 2014 at 3:54am*

**Calculus**

Posted by MG on Wednesday, March 26, 2014 at 6:54pm. The hands of a clock in some tower are 4.5m and 2m in length. How fast is the distance between the tips of the hands changing at 9:00? (Hint: Use the law of cosines) The distance between the tips of the hands is changing at ...
*Thursday, March 27, 2014 at 3:36am*

**Calculus**

If e^x = 243 and e^y = 32 then e^((3x + 4y)/5) =? The answer is 432, but I don't understand why.
*Thursday, March 27, 2014 at 3:34am*

**College Calculus**

Thank you for the response, i tried the method mentioned above three times and was incorrect each time, i double checked all my work to match the method above. The correct answer is always just .3 under the answer All of your arithmetic is right as well, so it is not that. ...
*Thursday, March 27, 2014 at 3:31am*

**pre calculus**

C(x) = 2.00 for 0 < x <= 1 2.00 + .20(10x) for 1 < x < 2 since there are 10 charging units per mile.
*Thursday, March 27, 2014 at 12:10am*

**pre calculus**

A taxi company charges $2.00 for the first mile (or part of a mile) and 20 cents for each succeeding tenth of a mile (or part). Express the cost C (in dollars) of a ride as a piecewise-defined function of the distance x traveled (in miles) for 0 < x < 2
*Thursday, March 27, 2014 at 12:07am*

**Calculus**

Thank you very much!
*Wednesday, March 26, 2014 at 11:46pm*

**Pre calculus**

yes. The reason the law of sines can give two triangles is because sin(x) is positive all the way from 0 to 180. cos(x) becomes negative for x>90, so the formula takes that into account, always leaving only one possible answer. I mean, think about it geometrically. If you ...
*Wednesday, March 26, 2014 at 11:46pm*

**Calculus**

Since velocity is the derivative of position, v(t) = -32t + 160 now just solve -32t+160 = 32 -32t+128 = 0 t = 4
*Wednesday, March 26, 2014 at 11:39pm*

**Calculus**

The height in feet above the ground of a ball thrown upwards from the top of a building is given by s=-16t^2 + 160t + 200, where t is the time in seconds. If the maximum height is 600 feet, what is v^-1(32)? The answer is supposed to be 4 seconds, but I don't understand ...
*Wednesday, March 26, 2014 at 11:07pm*

**argggh - Calculus**

messed up in my expansion volume should have been 4x^3- 120x^2 + 800x and V' = 12x^2 - 240x + 800 = 0 3x^2 - 60x + 200=0 to get x = 4.23
*Wednesday, March 26, 2014 at 10:11pm*

**Calculus**

First things first: width --- s length ---- 2s 2s^2 = 800 s^2 = 400 s = 20 so the piece of metal is 20 by 40 let the side of the square to be cut out be x so the width is 20-2x the length is 40-2x the height is x Volume = x(20-2x)(40-2x) = 2x^3 - 120x^2 + 800x d(Volume)/dx = ...
*Wednesday, March 26, 2014 at 10:05pm*

**Calculus **

You are given a piece of sheet metal that is twice as long as it is wide an has an area of 800m^2. Find the dimensions of the rectangular box that would contain a max volume if it were constructed from this piece of metal by cutting out squares of equal area at all four ...
*Wednesday, March 26, 2014 at 9:49pm*

**Calculus**

you should have recalled that sin (-x) = -sinx so that sin(-.1) could not have been positive. did you mean -.1 ?
*Wednesday, March 26, 2014 at 9:14pm*

**Calculus**

Use a tangent line approximation at x=0 to estimate the value of sin(-0.1). I got 0.1
*Wednesday, March 26, 2014 at 8:56pm*

**Calculus**

yes v(t) = h ' (t) = -16t + 5 so v(0) = -16(0) + 5 = 5
*Wednesday, March 26, 2014 at 8:54pm*

**Calculus**

The vertical position of an object is modeled by the function h(t)=-16t^2 +5t+7, where h is measured in feet and t is measured in seconds. Find the object's initial velocity (that is, the velocity at t=0). Is it 5 feet per second?
*Wednesday, March 26, 2014 at 8:46pm*

**Pre calculus**

For the most part, will a law of cosines always be one triangle? As in one triangle to solve?
*Wednesday, March 26, 2014 at 8:35pm*

**College Calculus**

let Ø be the angle between them the angular velocity of the minute hand = 2π/60 rad/min = π/30 rad/min the angular velicity of the hour hand = 2π/(12(60)) or π/720 rad/min then, so dØ/dt = (π/30 - π/720) rad/min dØ/dt = 23&#...
*Wednesday, March 26, 2014 at 8:25pm*

**College Calculus**

I followed this example, where am i missing something or going about it wrong? If we let y be the angle between the two hands and x be the distance between the two tips, then, by the law of cosines, we have: x^2 = 5^2 + 1.5^2 - 2*5*1.5cos(y) x^2 = 27.5 - 15cos(y) Take the ...
*Wednesday, March 26, 2014 at 6:58pm*

**College Calculus**

The hands of a clock in some tower are 4.5m and 2m in length. How fast is the distance between the tips of the hands changing at 9:00? (Hint: Use the law of cosines) The distance between the tips of the hands is changing at a rate of _______ m/hr at 9:00? I tried several times...
*Wednesday, March 26, 2014 at 6:54pm*

**Calculus**

dp/dt = v = 2 t at t = 2 v = 2*2 = 4
*Wednesday, March 26, 2014 at 4:26pm*

**Calculus**

If position is given by p(t)=t^2 +1, find the velocity v(t) at t = 2. I'm completely lost as to where to even start with this problem.
*Wednesday, March 26, 2014 at 4:25pm*

**Calculus**

I did one for you. Now you do this one. By the way you left the half life of carbon 14 or exponential decay function out of your statement of the problem making it impossible without looking that up.
*Wednesday, March 26, 2014 at 10:38am*

**Calculus**

12 = 40 e^(-kt) .3 = e^-30 k ln .3 = -30 k -1.20 = -30 k k = .04013 so .5 = e^-.04013 t -.6931 = -.04013 t t = 17.3 years
*Wednesday, March 26, 2014 at 10:35am*

**Calculus**

The amount of carbon-14 still present in a sample after t years is given by the function where C0 is the initial amount. Estimate the age of a sample of wood discovered by an archeologist if the carbon level in the sample is only 18% of its original carbon-14 level.
*Wednesday, March 26, 2014 at 10:31am*

**Calculus**

If 40 milligrams of strontium-90 radioactively decays to 12 milligrams in 30 years, find its half-life (the number of years it takes until half of it remains). Use the formula A = p ⋅ e−kt, where p is the amount and A the (smaller) final amount.
*Wednesday, March 26, 2014 at 10:29am*

**calculus**

A rectangular field is to be enclosed and divided into 4 equal lots by fences parallel to one of the sides. A total of 10,000 meters of fence are available. Find the area of the largest field that can be enclosed.
*Wednesday, March 26, 2014 at 10:15am*

**pre calculus**

-1 - 1/√3
*Wednesday, March 26, 2014 at 5:45am*

**pre calculus**

Find the exact values: tan(7pi/4) - tan (pi/6)
*Wednesday, March 26, 2014 at 1:42am*

**Calculus**

let the number be x, and the sum as stated be S S = x^2 + 1/x dS/dx = 2x - 1/x^2 = 0 for a max/min 2x = 1/x^2 2x^3 = 1 x^3 = 1/2 x = (1/2)^(1/3) or the cube root of 1/2
*Tuesday, March 25, 2014 at 9:47pm*

**Calculus**

Find a positive number such that the sum of the square of the number and its reciprocal is a minimum.
*Tuesday, March 25, 2014 at 9:25pm*

**Grade 12 Calculus**

thx!
*Tuesday, March 25, 2014 at 9:14pm*

**Grade 12 Calculus**

I hope your function looks something like this: R(x) = (5000 - 100x)(30 + x) = 150000+ 5000x - 3000x - 100x^2 = -100x^2 + 2000x + 150000 this is a standard parabola opening dowwards , so it will have a maximum the x of the vertex is -b/(2a) = -2000/-200 = 10 So there should be...
*Tuesday, March 25, 2014 at 9:06pm*

**Grade 12 Calculus**

For an outdoor concert, a ticket price of $30 typically attracts 5000 people. For each $1 increase in the ticket price, 100 fewer people will attend. The revenue, R, is the product of the number of people attending and the price per ticket. a) Let x represent the number of $1 ...
*Tuesday, March 25, 2014 at 8:46pm*

**Calculus - good catch bob**

Dang - forgot the restriction on the domain.
*Tuesday, March 25, 2014 at 8:35pm*

**Calculus**

now if you are allowed to remove trees, and for each tree removed, the average goes up by 5, then the optimal is to remove five trees.
*Tuesday, March 25, 2014 at 8:29pm*

**Calculus**

number apples=average*number trees let x be the nubmer of trees 50<x<inf number apples=(200-(x-50)*5)(x) where x is the number of trees, 50<x<infinity N=200x-5x^2 +250x dN/dx=0=200-10x+250 10x=450 x=45 but x>50, so look at optimal check x=50 N=50*200=10000 ...
*Tuesday, March 25, 2014 at 8:28pm*

**Grade 12 Calculus**

if the sheet is x by y, and is rolled along the y axis, 2x+2y = 100 v = pi r^2 y where 2pi r = x, or r = x/(2pi), so v = pi (x/(2pi))^2 (100-2x)/2 = x^2(50-x)/(4pi) dv/dx = x(100-3x)/(4pi) dv/dx=0 when x = 100/3 at that point, max v is pi*(50/3)^3
*Tuesday, March 25, 2014 at 8:21pm*

**Calculus**

the number of apples is yield/tree * # trees. With x trees, yield per tree is 200 - 5(x-50) for x > 50 So, total crop is c(x) = x(200-5(x-50)) = x(450-5x) = 450x - 5x^2 c'(x) = 450-10x c' = 0 at x=45 So, the max yield is achieved with 45 trees
*Tuesday, March 25, 2014 at 8:16pm*

**Calculus**

There are 50 apple trees in an orchard, and each tree produces an average of 200 apples each year. For each additional tree planted within the orchard, the average number of apples produced drops by 5. What is the optimal number of trees to plant in the orchard? I mostly need ...
*Tuesday, March 25, 2014 at 8:09pm*

**Grade 12 Calculus**

A rectangular piece of paper with perimeter 100 cm is to be rolled to form a cylindrical tube. Find the dimensions of the paper that will produce a tube with maximum volume. I have made it up to getting an equation for V(w).
*Tuesday, March 25, 2014 at 7:49pm*

**Calculus Rate of Change**

average=(finalvalue-initial value)/chngeinX final value= h'(6)=4*6=24 initial vealue=h'(2)=4*2=8 average h'=16/4=4 units unknown
*Tuesday, March 25, 2014 at 10:52am*

**Calculus Rate of Change**

Find the average rate of change h(x)=2x^2-4 from x=2 to x=6 Simplify your answer as much as possible
*Tuesday, March 25, 2014 at 10:27am*

**calculus**

v = 4π/3 r^3 v' = 4π r^2 at r=50, v = 500π/3 and v' = 100π So, the tangent line at r=50 is v - 500π/3 = 100π(x-50)
*Tuesday, March 25, 2014 at 4:58am*

**Calculus**

recall that the voulme of a sphare of radius r is v(r)=(4pir^3)/3. find l, ther linearisation of v(r) at r=50. A sphare of radius 50 centimeters is covered with a layer of point of thickness 0.31 millimeters. use the linearisation of v at r=50 to estimate the volume of point ...
*Tuesday, March 25, 2014 at 2:13am*

**calculus**

Recall that the volume of a sphere of radius r is V(r) =4\, \pi\, r^3 /3. Find L, the linearisation of V(r) at r=50
*Tuesday, March 25, 2014 at 2:05am*

**Trigonometry**

http://www.wolframalpha.com/input/?i=y%3D2sin%28x-2pi%2F3%29 for x-intercepts, y = 0 2sin(x-2pi/3) = 0 sin(x-2pi/3)=0 but sin 0 = 0 and sin π =0 and sin 2π = 0 so x - 2π/3 = 0 and x -2π/3 = π and x - 2π/3 = 2π x = 2π/3 or x = &#...
*Tuesday, March 25, 2014 at 12:11am*

**Calculus**

fre
*Monday, March 24, 2014 at 11:59pm*

**Calculus**

x + 4xy = y^2 1 + 4y + 4xy' = 2yy' y' = (1+4y)/(2y-4x)
*Monday, March 24, 2014 at 11:59pm*

**Calculus A**

h' = (x^2-2x-9)/(x-1)^2 h" = 20/(x-1)^3 Clearly there are no inflection points, since f" is never zero h' is zero at two places, since the numerator is. So, there will be two extrema, one on each side of x=1. So, one will be a max, the other a min, depending ...
*Monday, March 24, 2014 at 11:58pm*

**Calculus A **

Find all relative extrema and points of inflection for the function; h(x)=(x^2+5x+4)/(x-1)
*Monday, March 24, 2014 at 11:20pm*

**Calculus **

Find dy/dx implicitly in terms of x and y only for the following function; x+ 4xy=y^2
*Monday, March 24, 2014 at 11:17pm*

**Calculus**

17
*Monday, March 24, 2014 at 8:47pm*

**Calculus A**

I will assume you meant: h(x) = x^2 + 5x + 4/(x-1) h ' (x) = 2x + 5 - 4/(x-1)^2 = 0 for max/min 2x + 5 = 4/(x-1)^2 (2x+5)(x^2 - 2x + 1) = 4 2x^3 - 4x^2 + 2x + 5x^2 - 10x + 5 = 4 2x^3 + x^2 - 8x + 1 = 0 hard to solve, Wolfram has this http://www.wolframalpha.com/input/?i=2x...
*Monday, March 24, 2014 at 7:32pm*

**Calculus A **

Find all relative extrema and points of inflection for the following function... h(X)= X^2+5X+4/ X-1 min= max= inflection points=
*Monday, March 24, 2014 at 7:16pm*

**Calculus**

Nevermind I didn't read the question correctly. I got it! Thank You!
*Monday, March 24, 2014 at 1:43am*

**Calculus**

after this, i am to solve the differential but I am confused as to what I would make T air. dT/dt=-k(45-Tair) what do i do with the other 2 variables since k is a constant of proportionality. and T air is a constant
*Monday, March 24, 2014 at 12:49am*

**Calculus 12 Optimization**

120
*Sunday, March 23, 2014 at 9:35pm*

**calculus**

Assuming an initial position of zero, s(t) = 5/2 t^2 for 0<=t<1 so, at t=1, s = 5/2 Now, using the 2nd function, s(t) = 5/2 + 4t^(3/2) - log(t) solve that for s(t) = 4
*Sunday, March 23, 2014 at 8:21pm*

**Calculus**

use implicit differentiation: x/2 + y/8 y' = 0 y' = -4x/y
*Sunday, March 23, 2014 at 8:18pm*

**calculus**

Suppose that a particle moves along a line so that its velocity v at time t is given by this piecewise function: v(t)=5t if 0≤t<1 v(t)=6((t)^(1/2))-(1/t) if 1≤t where t is in seconds and v is in centimeters per second (cm/s). Estimate the time(s) at which the ...
*Sunday, March 23, 2014 at 8:17pm*

**Calculus**

Find the slope of the tangent line to the ellipse x^2/4 + y^2/16= 1 at the point (x,y)
*Sunday, March 23, 2014 at 8:11pm*

**Calculus**

the heat flow is proportional to the difference in temperature. dT/dt= -k(T-Tair) T air is a constant,
*Sunday, March 23, 2014 at 7:24pm*

**Calculus**

Suppose you have a hot cup of coffee in a room where the temp is 45 Celcius. Let y(t) represent the temp. of coffee as a function of the number of minutes t that have passed since the coffee was poured a) write a differential equation that applies to newtons law of cooling. ...
*Sunday, March 23, 2014 at 6:16pm*

**CALCULUS ECONOMICS**

How did you get to that number?I have 5000 (wrong solution) and I can't figure out q7 because i don't know the right value for q.opt (q.eq=625?)
*Sunday, March 23, 2014 at 3:21pm*

**CALCULUS ECONOMICS**

And for q7??It's my last chance...
*Sunday, March 23, 2014 at 2:46pm*

**CALCULUS ECONOMICS**

right for Q6!!!!!!!thankssssss
*Sunday, March 23, 2014 at 2:26pm*

**CALCULUS ECONOMICS**

2750? right or wrong?
*Sunday, March 23, 2014 at 10:55am*

**CALCULUS ECONOMICS**

Yes, they are right! Have you the answers of question 5,6,7? Thanks very very much!
*Sunday, March 23, 2014 at 9:13am*

**CALCULUS ECONOMICS**

Nothing?I need a clue in this one!
*Sunday, March 23, 2014 at 6:54am*

**CALCULUS ECONOMICS**

thanks
*Sunday, March 23, 2014 at 4:55am*

**CALCULUS ECONOMICS**

QUESTION: In this case, what is the difference between the optimal level of total consumption and the level of total consumption in equilibrium?
*Sunday, March 23, 2014 at 4:18am*

**CALCULUS ECONOMICS**

If Q = 440, shouldn't P = 560?
*Sunday, March 23, 2014 at 1:55am*

**Calculus Help Please!!!**

6x^2 + 9y^2 y' = 0 y' = -2x^2 / 3y^2 now for y", do it again: 12x + 18y (y')^2 + 9y^2 y" = 0 y" = -2(2x+3y(y')^2) / 3y^2 Now just substitute in y' and you're done Or, you can use the quotient rule on y': y' = -2/3 (x^2 / y^2) y&...
*Saturday, March 22, 2014 at 4:02pm*

**Calculus Help Please!!! **

find y' and y” by implicit differentiation. 2x^3 + 3y^3 = 8
*Saturday, March 22, 2014 at 3:53pm*

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